An equilateral triangle has a side length of 10 inches. find the length of the triangle altitude

An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.

It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a (the altitude) ^2+5 (the base) ^2=10 (the hypotenuse) ^2

A^2+5^2=10^2

A^2+25=100

A^2=75

A=sqrt (75)

A=5*sqrt (3)

Final answer:

The altitude of an equilateral triangle with side length 10 is 5sqrt (3), or about 8.66